A Galaxy-like perturbation of the Robertson–Walker metric

The standard procedure for finding analytic perturbations in General Relativity suffers from the drawback that it is cumbersome to use beyond linear order perturbations. We present an alternate method of finding perturbations and provide an example in the form of a spherically symmetric over-dense region in an open Robertson–Walker background. The perturbation has several properties which are similar to those of a spiral galaxy.     

静磁场中双极化态弱平面引力波对高斯束的扰动能量

讨论了处于静磁场中双极化态弱平面引力波对高斯束的一阶和二阶扰动能量，数值计算表明，引力波对整个电磁体系的能量扰动很小.换言之，背景电磁场在引力波作用下其总能量不会发生明显改变，但在局部区域中产生的扰动能流则可能引起可供观测的效应. 关键词： 双极化态弱平面引力波 高斯束 电磁响应 扰动能量     

New equation for the description of inelastic interaction of nonlinear localized waves in dispersive media

A wave equation for the simulation of nonlinear plane solitary perturbations of the free surface of a shallow fluid has been derived. In contrast to the modified Boussinesq equation, the new one correctly describes the interaction of counter-propagating small-amplitude waves. It has been shown analytically that collisions of solitons are inelastic even in the first-order perturbation theory and the nonlinear dynamics of such collisions is qualitatively different from that described by the modified Boussinesq equation.     

Gravitational perturbations of spherically symmetric systems. II. Perfect fluid interiors

Methods developed in a previous paper on perturbations of the Schwarzschild metric are here extended to the treatment of perturbations of perfect fluid stellar models. The perturbations of a perfect fluid sphere are explicitly decomposed into their gauge invariant and gauge dependent parts and a variational principle for the perturbation equations is derived. The Hamiltonian for the perturbations is constructed and a sufficient condition for stability against nonradial, radiative perturbations is derived from it. The stability criterion is applied to two interesting classes of stellar models, polytropic white dwarf models and high-density neutron star cores with pressure proportional to energy density.     

Second-order filtering and sensing with partially coupled traveling waves in a single resonator

The counterpropagating waves in a single traveling-wave cavity can be partially coupled by means of a small perturbation such as a notch. When it is side coupled to a waveguide, this single cavity yields a general second-order (Chebyshev) reflection response in the waveguide, which is useful for narrow-bandwidth reflecting applications. In a different application, the cavity amplifies small reflections induced by external perturbations, thus finding use in ultrafine sensing. Amplification factors as great as 10(12) are predicted for the highest-Q microsphere resonators. The analytic theory of these devices is presented.     

Reheating in tachyonic inflationary models: Effects on the large scale curvature perturbations

We investigate the problem of perturbative reheating and its effects on the evolution of the curvature perturbations in tachyonic inflationary models. We derive the equations governing the evolution of the scalar perturbations for a system consisting of a tachyon and a perfect fluid. Assuming the perfect fluid to be radiation, we solve the coupled equations for the system numerically and study the evolution of the perturbations from the sub-Hubble to the super-Hubble scales. In particular, we analyze the effects of the transition from tachyon driven inflation to the radiation dominated epoch on the evolution of the large scale curvature and non-adiabatic pressure perturbations. We consider two different potentials to describe the tachyon and study the effects of two possible types of decay of the tachyon into radiation. We plot the spectrum of curvature perturbations at the end of inflation as well as at the early stages of the radiation dominated epoch. We find that reheating does not affect the amplitude of the curvature perturbations in any of these cases. These results corroborate similar conclusions that have been arrived at earlier based on the study of the evolution of the perturbations in the super-Hubble limit. We illustrate that, before the transition to the radiation dominated epoch, the relative non-adiabatic pressure perturbation between the tachyon and radiation decays in a fashion very similar to that of the intrinsic entropy perturbation associated with the tachyon. Moreover, we show that, after the transition, the relative non-adiabatic pressure perturbation dies down extremely rapidly during the early stages of the radiation dominated epoch. It is these behavior which ensure that the amplitude of the curvature perturbations remain unaffected during reheating. We also discuss the corresponding results for the popular chaotic inflation model in the case of the canonical scalar field.     

Shock wave formation in hot nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.     

光纤中扰动的小信号增益

从非线性薛定谔方程出发,在小信号近似下,推导并求解了光纤中扰动相位和幅度的演化方程,利用得到的扰动相位及功率增益的表达式,研究了初相位和频率对传输过程中扰动增益的影响。研究表明：扰动的初相位对扰动增益的初值和初始阶段的演化规律有重要影响;取决于扰动初相位,任何一个频率的扰动增益都有可能达到一个共同的最大值;在被认为无调制不稳定的正色散区和扰动频率大于截止频率的负色散区,扰动增益随距离是振荡的;在被认为有调制不稳定的扰动频率小于截止频率的负色散区,频率相同而初相位不同的扰动增益将经历不同形式的演化后趋于同一正值。     

Calculation of the higher-order perturbations in the theory of gamma transport

The higher-order perturbations in the application of perturbation theory to the -transport equation are discussed. An analytic expression is obtained for the perturbation flux of arbitrary order arising from a variation in the electron density of the medium, regardless of its geometry. This expression can be used in the constant-cross-section approximation to find the perturbation due to a change in the chemical composition of a plane layer. The numerical calculation is illustrated with an example.The author thanks S. B. Shikhov for interest in this study.     

Rows of optical vortices from elliptically perturbing a high-order beam

An optical vortex (phase singularity) with a high topological strength resides on the axis of a high-order light beam. The breakup of this vortex under elliptic perturbation into a straight row of unit-strength vortices is described. This behavior is studied in helical Ince-Gauss beams and astigmatic, generalized Hermite-Laguerre-Gauss beams, which are perturbations of Laguerre-Gauss beams. Approximations of these beams are derived for small perturbations, in which a neighborhood of the axis can be approximated by a polynomial in the complex plane: a Chebyshev polynomial for Ince-Gauss beams, and a Hermite polynomial for astigmatic beams.     

LiNbO3晶体-熔体界面的失稳及向胞状界面演化的实验研究

利用周期旋转生长条纹作为时标(timemarker),研究了直拉法掺钇LiNbO₃的各向异性生长系统中晶体-熔体界面的失稳及向胞状界面的演化。测得平界面失稳的临界条件,观测到失稳初期的界面上存在的两种干扰,即正弦式干扰和正弦式行波干扰。实验结果表明,平界面失稳后,经历正弦干扰、干扰振幅的增长、干扰的小面化、干扰的合并,最后演化为稳态胞状界面。实验观测还表明,稳态胞状界面的波长甚大于界面初始干扰的波长,且为初始干扰波长的整数倍;以及同一系统中平界面向胞状界面转变的临界生长速度小于胞状界面向平界面转变的临界速度,这表明小面化的胞比非小面的平面更为稳定。 关键词：     

Evolution of local ideal helical perturbations in cylindrical plasma

The evolution of a local helical perturbation and its stability property for arbitrary magnetic shear configurations are investigated for the case of in cylindrical geometry. An analytic stability criterion has been obtained which predicts that a strong magnetic shear will enhance the instability in the positive shear region but enhance the stability in the negative shear region. The perturbations with the poloidal and toroidal perturbation mode numbers m/n=1/1 is most unstable due to the stabilizing terms increasing with m. For m/n=1/1 local perturbations in the conventional positive magnetic shear (PMS) configurations, a larger q_{min} exhibits a weaker shear in the core and is favourable to the stability, while in the reversed magnetic shear (RMS) configurations, a larger q_0 corresponds to a stronger positive shear in the middle region, which enhances the instability. No instabilities are found for m≥2 local perturbations. The stability for RMS configuration is not better than that for PMS configuration.     

Heat capacities of the dipolar Yukawa model polar fluid

The Stockmayer fluid is often used to describe a polar fluid. The dipolar Yukawa (DY) fluid is also a useful model for such fluids and is convenient for theoretical applications. Here we use the mean spherical approximation (MSA) and perturbation theory (PT) to study the heat capacities of the DY fluid model of a polar fluid and compare these results with Monte Carlo simulations for this model polar fluid. We find that the DY fluid shows the same features as the Stockmayer fluid does; demonstrating the utility of the DY fluid and further finding that the MSA and PT approaches give reasonably accurate results for the heat capacity.     

Non-Real Eigenvalues for {{\mathcal{PT}}}-Symmetric Double Wells

We study small, \({{\mathcal{PT}}}\)-symmetric perturbations of self-adjoint double-well Schrödinger operators in dimension \({n\ge 1}\). We prove that the eigenvalues stay real for a very small perturbation, then bifurcate to the complex plane as the perturbation gets stronger.     

Rayleigh-Taylor instability experiments with precise and arbitrary control of the initial interface shape

In a Rayleigh-Taylor instability a dense fluid sits metastably atop a less dense fluid, a configuration that can be stabilized using a magnetic field gradient when one fluid is highly paramagnetic. On switching off the magnetic field, the instability occurs as the dense fluid falls under gravity. By affixing appropriately shaped magnetically permeable wires to the outside of the cell, one may impose arbitrarily chosen and well-controlled initial perturbations on the interface. This technique is used to examine both the linear and nonlinear growth regimes for which the perturbation amplitudes, growth rates, and nonlinear growth coefficients are obtained.     

Microscopic-scale simulations of macroscopic flow patterns in non-equilibrium two-dimensional systems

Summary We have used a molecular-dynamics simulation for reproducing the behaviour of a two-dimensional fluid flow submitted to external perturbations and embedded in a non-inertial reference frame. This simple model has been used to verify current hypotheses on the causes generating a cyclonic circulation in the North Tyrrhenian basin, provided one uses suitable perturbation strenghts scaled from the real-world dynamics. Results put in evidence that the onset of a stationary cyclonic circulation which superimposes to the S-N flow requires the simultaneous presence of an orthogonal and an anti-parallel stream. This finding is in agreement with the hypotheses suggested by a preliminary analysis of experimental data. The limits of such models are discussed together with possible extensions to reproduce mesoscopic systems, in order to simulate the coexistence of large- and small-scale dynamics. The model is particularly suited to deal with boundary conditions of general analytical shapes.     

Gravitational perturbations in the expanding universe in a coordinate representation

Gravitational perturbations in the expanding universe are analyzed within the framework of Newtonian cosmology. In contrast to classical work, the perturbations are found not in a Fourier but in a coordinate representation. This makes it possible to obtain general expressions for finding the distributions of perturbations in the density and velocity of matter as a function of the coordinates and time from the known distribution at the initial time. In the simplest cases of plane-symmetric and spherically symmetric distributions, analytical equations are obtained for density perturbations as a function of the coordinates and time. The final conclusion is that it is possible for gravitational perturbations to grow even when the characteristic size of a perturbation is less than the Jeans wavelength. Kazan’ State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 45–52, March, 1997.     

A finsler perturbation of the Poincaré metric

One method of gaining some insight into Finsler geomety is that of studying small Finsler perturbations of Riemannian metrics. We consider here the the standard two-dimensional upper half plane Poincaré metric, for which the geodesics are semi-circles and vertical lines. The effect of a simple Finsler perturbation on these geodesics is given by an explicit computation of the perturbed geodesics.